# Question #22549

Dec 20, 2017

Please see the processed steps below;

#### Explanation:

Probability of $3$ posts selected is $\frac{3}{9} = \frac{1}{3}$

Probability of none selected is $\frac{9 - 3}{9} \mathmr{and} \left(1 - \frac{1}{3}\right)$

$\frac{9 - 3}{9}$

$\frac{6}{9}$

$\frac{2}{3}$

Hence;

Probability of none selected is $= \frac{2}{3}$

Jan 2, 2018

$\frac{2}{3}$

#### Explanation:

$9$ applicants , $3$ posts
so probability of anyone selected at any post is $\frac{3}{9} = \frac{1}{3}$
so, probability that the same person is not selected can be easily identified
$P \left(s\right) + P \left(n\right) = 1$ where $P \left(s\right)$ means selected and $P \left(n\right)$ means not selected )
$\frac{1}{3} + P \left(n\right) = 1$
$P \left(n\right) = 1 - \frac{1}{3}$
$P \left(n\right) = \frac{3 - 1}{3}$
$P \left(n\right) = \frac{2}{3}$
Cheers!
If the question is that none of them is selected , then we woupd require probability of selection of each which on an average would not be greater than $\frac{1}{3}$.
My interpretion of question is that we need to find the probability of anyone not being selected .

It might require use of linear inequalities if the question isn't what i interpret .

for more please see my hand written script below 